Thanks for sharing the photos. Glad to see you're able to pull of some impressive feats with this gpu!
It's worth noting that most of the games, you are sacrificing detail where needed to achieve 60fps. As well, I still have doubts that 60fps is achieved in sequences with action, like for instance in CS:GO. Doubling the amount of pixels will only create more issues. However, that's not really the point.
Technically, your card can output to 1440p but in my honest opinion, you're going to have a bad time.
You can easily test this yourself prior to purchasing a new monitor by going into the Control Panel & super sampling to 1440p. I'm not sure if your GPU has access to these features but I would assume so.
My safe recommendation, without knowing the specs of your rig, is to upgrade to a 1050ti or similar card. As you will not have to worry about the PSU or any other replacements. Technically not a 1440p card but it will easily handle the games you play. I run a GTX 780 which is about equivalent to a GTX 1050ti in terms of game performance, and most of my games, with tweaks, run above 60fps at 1440p.
Edit: If you're using DVI-D, you can run higher than 60hz but you will run into issues as indicated here: